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Thomas Kruse
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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
M Hutzenthaler, A Jentzen, T Kruse, TA Nguyen
SN Partial Differential Equations and Applications 1 (2), 1-34, 2020
1922020
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
M Hutzenthaler, A Jentzen, T Kruse, T Anh Nguyen, P von Wurstemberger
Proceedings of the Royal Society A 476 (2244), 20190630, 2020
1292020
BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration
T Kruse, A Popier
Stochastics 88 (4), 491-539, 2016
1002016
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic …
E Weinan, M Hutzenthaler, A Jentzen, T Kruse
Journal of Scientific Computing 79 (3), 1534-1571, 2019
832019
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
M Hutzenthaler, A Jentzen, T Kruse
Partial Differential Equations and Applications 2 (6), 1-31, 2021
77*2021
Optimal control of an epidemic through social distancing
T Kruse, P Strack
Available at SSRN 3581295, 2020
762020
BSDEs with singular terminal condition and a control problem with constraints
S Ankirchner, M Jeanblanc, T Kruse
SIAM Journal on Control and Optimization 52 (2), 893-913, 2014
712014
Optimal stopping with private information
T Kruse, P Strack
Journal of Economic Theory 159, 702-727, 2015
692015
Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard …
C Beck, F Hornung, M Hutzenthaler, A Jentzen, T Kruse
Journal of Numerical Mathematics 28 (4), 197-222, 2020
622020
Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities
M Hutzenthaler, T Kruse
SIAM Journal on Numerical Analysis 58 (2), 929-961, 2020
612020
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
M Hutzenthaler, A Jentzen, T Kruse
Foundations of Computational Mathematics 22 (4), 905-966, 2022
532022
Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting
T Kruse, A Popier
Stochastic Processes and their Applications 126 (9), 2554-2592, 2016
492016
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
M Hutzenthaler, A Jentzen, T Kruse, TA Nguyen
arXiv preprint arXiv:2009.02484, 2020
262020
Optimal position targeting with stochastic linear-quadratic costs
S Ankirchner, T Kruse
Banach Center Publ 104 (1), 9-24, 2015
252015
Lp-solution for BSDEs with jumps in the case p<2: Corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general …
T Kruse, A Popier
Stochastics 89 (8), 1201-1227, 2017
232017
A verification theorem for optimal stopping problems with expectation constraints
S Ankirchner, M Klein, T Kruse
Applied Mathematics & Optimization 79, 145-177, 2019
182019
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
M Hutzenthaler, T Kruse, TA Nguyen
Journal of Mathematical Analysis and Applications 507 (1), 125761, 2022
162022
Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models
J Ackermann, T Kruse, M Urusov
Finance and Stochastics 25 (4), 757-810, 2021
162021
An inverse optimal stopping problem for diffusion processes
T Kruse, P Strack
Mathematics of Operations Research 44 (2), 423-439, 2019
15*2019
Numerical approximation of irregular SDEs via Skorokhod embeddings
S Ankirchner, T Kruse, M Urusov
Journal of Mathematical Analysis and Applications 440 (2), 692-715, 2016
152016
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